Linkedin hasn't replaced cold email, but it has become its indispensable partner, it's no longer about choosing one over the other, but about using them together to compensate for each other's weaknesses, email gives you massive reach and the ability to scale, while linkedin provides professional context and instant trust, ensuring the conversation doesn't start cold.
Data shows that LinkedIn generates significantly higher response rates than email, but keep in mind that email has a much lower cost per contact, allowing you to test and scale messages at a speed that LinkedIn doesn't offer, most email conversions come from follow up emails, and these multi step sequences are precisely what LinkedIn doesn't allow you to do at scale.
The strategy that truly works today is to unify both channels in a single sequence, first, you connect on linkedin with a personalized message, once they accept, you send them a detailed email to elaborate on the proposal, if they don't respond, you reach out to them on linkedin to remind them of your message, this combination makes LinkedIn the channel that builds initial trust, allowing email to then do its job effectively, the key isn't choosing, it's coordinating.